Both Jeff and Darius posted a link to a game called Dice Wars. They both like it. Jeff actually posted a rather detailed analysis - probably more detailed than the designer originally conceived. :D
I don't like the game. And the reason is simple: I'm a control freak.
It's not that I want to control everything. Micromanagement pisses me off. I just want to be able to rely on things. I want my success or failure to be more about my skill than whether or not I happen to find a four-leaf clover.
This actually relates to my previous post: I run the kinds of games I like. And I like the kinds of games where a choice you make now will have an effect on the game later.
The CHOICE you make now. Sure, a die roll or a piece of luck can (and even should) factor in. But the choice, for me, is the critical part. I like finding the optimum route, not finding a decent route and crossing my fingers. I like to prove my brain exists for a reason other than feeding change into slot machines.
There's a huge draw to luck, and I'm certainly not immune. I love playing Bang! and other hidden-card games (poker, spades, bridge). These are games in which luck is a critical factor.
But it isn't the dominant factor. The dominant factor is choosing how much to commit to your hand. If you have shitty luck, the game is not to win, but to take a minimum loss. If you have great luck, the game is not to win, but to take a maximum win. And if you overplay, that's your own damn fault, not luck.
A comparison would be if Dice Wars was played in ten-game sets where you could spend chips to gain more dice, and every region you ended with got you more chits. Instead of simply winning or losing based on luck, you would win or lose based on how you played a given lay.
This feeds into stages, actually, which is amusing. That's a complex subject, and there's several different ways to think about "stages". I'll probably post about them some other time. It sounds like at least one person might read it, and I have been thinking about it. (It's rather central to Gun Shy's design. It, by the way, is done save for debugging.)
Anyhow, my basic use for luck is not in determining a win or a loss, but in determining the amplitude or approach to a win or loss. You, the player, should be responsible for the decisions which bring about a win or a loss. The dice shouldn't be able to turn a win into a loss... or a loss into a win.